共查询到17条相似文献,搜索用时 140 毫秒
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本文讨论了力学中出现的一类4×4无界Hamilton算子矩阵的本征向量组的块状Schauder基性质.在一定的条件下, 考虑了此类Hamilton算子矩阵的本征值问题, 进而给出了其本征向量组是某个Hilbert空间的一组块状Schauder基的一个充要条件,并通过矩形薄板的自由振动和弯曲问题验证了所得结果的有效性. 相似文献
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研究了Sturm-Liouvile偏微分方程导出的无穷维Hamilton算子的本征值问题.证明了导出的无穷维Hamilton算子族本征函数系的完备性,为对此类方程应用基于Hamilton体系的分离变量法提供了理论基础.最后举例说明了结果的有效性. 相似文献
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无穷维Hamilton算子的二次数值域 总被引:2,自引:0,他引:2
研究了一类无界无穷维Hamilton算子的二次数值域的性质,进而,应用二次数值域来刻画了无穷维Hamilton算子谱的分布范围,并给出了二次数值域的闭包包含谱集的结论. 相似文献
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本文讨论了一类在弦和梁的微小振动中出现的二次算子族L(λ)=λ~2MλK-A的谱分布问题,进而将所得结论与无穷维Hamilton算子联系起来,利用无穷维Hamilton算子的特殊结构,得到了一类非负无穷维Hamilton算子的谱分布,这为无穷维Hamilton算子的半群方法提供了理论保证. 相似文献
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《应用泛函分析学报》2016,(4)
借助于Hilbert空间上的正算子,给出算子值赋范线性空间的概念,进而讨论了一类特殊的算子值Banach空间上Schauder基的性质,并给出Schauder基和弱Schauder基的等价刻画. 相似文献
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The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness
of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones
are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the
pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a
connection between the energetic stability condition and a perturbation problem for the coefficients is given. 相似文献
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In this paper we consider a class of hybrid systems induced by operator valued measures. This includes semigroups of operators perturbed by bounded as well as unbounded operator valued measures. We construct an evolution operator for the hybrid system and based on its properties we prove existence, uniqueness and regularity properties of solutions. We also consider Semilinear Problems driven by vector measures. Nonstandard problems arising in the study of the classical linear quadratic regulator problem in the present setting are discussed and partial solutions provided. 相似文献
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V. N. Pivovarchik 《Ukrainian Mathematical Journal》2007,59(5):766-781
We consider a class of quadratic operator pencils that occur in many problems of physics. The part of such a pencil linear
with respect to the spectral parameter describes viscous friction in problems of small vibrations of strings and beams. Patterns
in the location of eigenvalues of such pencils are established. If viscous friction (damping) is pointwise, then the operator
in the linear part of the pencil is one-dimensional. For this case, rules in the location of purely imaginary eigenvalues
are found.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 5, pp. 702–716, May, 2007. 相似文献
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经典量子系统的哈密尔顿是自伴算子.哈密尔顿算符的自伴性不仅确保了系统遵循酉演化,而且也保证了它自身具有实的能量本征值.但是,确实有一些物理系统,其哈密尔顿是非自伴的,但也具有实的能量本征值,这种具有非自伴哈密尔顿的系统就是非自伴量子系统.具有伪自伴哈密尔顿的系统是一类特殊的非自伴量子系统,其哈密尔顿相似于一个自伴算子.本文研究伪自伴量子系统的酉演化与绝热定理.首先,给出了伪自伴算子定义及其等价刻画;其次,对于伪自伴哈密尔顿系统,通过构造新内积,证明了伪自伴哈密尔顿在新内积下是自伴的,并给出了系统在新内积下为酉演化的充分必要条件.最后,建立了伪自伴量子系统的绝热演化定理及与绝热逼近定理. 相似文献
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Christian Wyss 《Journal of Functional Analysis》2010,258(1):208-592
For a class of unbounded perturbations of unbounded normal operators, the change of the spectrum is studied and spectral criteria for the existence of a Riesz basis with parentheses of root vectors are established. A Riesz basis without parentheses is obtained under an additional a priori assumption on the spectrum of the perturbed operator. The results are applied to two classes of block operator matrices. 相似文献
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Marianna A. Shubov 《Mathematische Nachrichten》2002,241(1):125-162
We develop spectral and asymptotic analysis for a class of nonselfadjoint operators which are the dynamics generators for the systems governed by the equations of the spatially nonhomogeneous Timoshenko beam model with a 2–parameter family of dissipative boundary conditions. Our results split into two groups. We prove asymptotic formulas for the spectra of the aforementioned operators (the spectrum of each operator consists of two branches of discrete complex eigenvalues and each branch has only two points of accumulation: +∞ and —∞), and for their generalized eigenvectors. Our second main result is the fact that these operators are Riesz spectral. To obtain this result, we prove that the systems of generalized eigenvectors form Riesz bases in the corresponding energy spaces. We also obtain the asymptotics of the spectra and the eigenfunctions for the nonselfadjoint polynomial operator pencils associated with these operators. The pencil asymptotics are essential for the proofs of the spectral results for the aforementioned dynamics generators. 相似文献
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Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils 下载免费PDF全文
In this article we are interested in the numerical computation of spectra of
non-self adjoint quadratic operators. This leads to solve nonlinear eigenvalue problems. We begin with a review of theoretical results for the spectra of quadratic operators, especially for the Schrödinger pencils. Then we present the numerical methods developed to compute the spectra: spectral methods and finite difference discretization, in infinite or in bounded domains. The numerical results obtained are analyzed
and compared with the theoretical results. The main difficulty here is that we have to
compute eigenvalues of strongly non-self-adjoint operators which are very unstable. 相似文献